Answer:
Step-by-step explanation:
I want to start with a quick explanation of slope/ rate of change since you say you don't get it at all. Basically it measures how fast something changes. Or, in other words, if x changes by so much, y will change by a corresponding amount.
If you look at the graph of just y=x, you can see that as x changes by 1 so does y. if you make it y=2x, will x=1 makes y=2, and x = 2 makes y = 4, so here it changes by 2. You cans ee it keeps going in that manner. Also notice these make straight lines, maybe not horizontal, but still straight diagonal lines. This is important for a constant slope.
The way slope can be describes is "rise over run" also. Which means you count how many you "rise" and divide it by how many you "run", or in other words how your y values change and your x values change. Using y = -.5x this time let's see what we get using this rise over run idea. It's usually easier to compute the "run" first, so let's say we move from 2 to 4. That makes our run 2, keep that in mind. the y values that correspond to this are -.5*2 = -1 and -.5*4 = -2 note we keep the negative signs here. Now that we have the y values what are the change in them? well to go from -1 to -2 is -1, so our change in y is -1.
As I started with the rise over run is change in y divided by change in x. we found both of those so our slope is -1/2 so negative one half. That's just an example to hopefully clear up any confusion about slope.
The first part of your question I'm not sure about. Are any numbers given at all anywhere? the y looks longer than x but we can't really say exactly how long. We can tell the slope is negative at least, since it points downward going from left to right, but I don't think we can say what the exact rate of change (slope) is.
The second part uses the first so hard to say. If you can find what the rate of change is the answer will basically be (delta y) = (rate of change)*(delta x) since rate of change = (delta y)/(delta x) since delta means "change in"
The third gives some numbers, but we would still need the rate of change. I'll give the best answer I can. I do want to say that putting slope into an equation will often be represented by the letter m.
Anyway, pretending we know what m is, the method to find the equation of y is to use the formula y - y1 = m(x - x1). x1 and y1 are the coordinates of a point that you need. And int he question they give you one. So we will plug in.
y - y1 = m(x - x1)
y - (-2.5) = m(x - 1) Then distribute that m we're pretending we know
y - (-2.5) = mx - m Then get y by itself
y = mx - m - 2.5
So once you know m you can solve everything else. If you can find something that says how long those red and blue lines are, or maybe the points they point from and to you can let me know. Hopefully this helpped though.
